{"title":"Permutation Invariant Individual Batch Learning","authors":"Yaniv Fogel, M. Feder","doi":"10.1109/ITW55543.2023.10161673","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161673","url":null,"abstract":"This paper considers the individual batch learning problem. Batch learning (in contrast to online) refers to the case where there is a \"batch\" of training data and the goal is to predict a test outcome. Individual learning refers to the case where the data (training and test) is arbitrary, individual. This batch individual setting poses a fundamental issue of defining a plausible criterion for a universal learner since in each experiment there is a single test sample. We propose a permutation invariant criterion that, intuitively, lets the individual training sequence manifest its empirical structure for predicting the test sample. This criterion is essentially a min-max regret, where the regret is based on a leave-one-out approach, minimized over the universal learner and maximized over the outcome sequences (thus agnostic). To show its plausibility, we analyze the criterion and its resulting learner for two cases: Binary Bernoulli and 1-D deterministic barrier. For both cases the regret behaves as O(c/N), N the size of the training and c = 1 for the Bernoulli case and log4 for the 1-D barrier. Interestingly, in the Bernoulli case, the regret in the stochastic setting behaves as O(1/2N) while here, in the individual setting, it has a larger constant.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121379948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Role of the Alphabet in Network Coding: An Optimization Approach","authors":"Christopher Hojny, A. B. Kilic, A. Ravagnani","doi":"10.1109/ITW55543.2023.10161662","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161662","url":null,"abstract":"We consider the problem of determining the one-shot, zero-error capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on a mixed-integer program, which computes the size of the largest unambiguous codebook for a given alphabet size. As an application of our approach, we recover, extend and refine various results that were previously obtained with case-by-case analyses or specialized arguments, giving evidence of the wide applicability of our approach. We also provide two simple ideas that reduce the complexity of our method for some families of networks. We conclude the paper by outlining a research program we wish to pursue to investigate the one-shot capacity of large networks affected by adversarial noise and, more generally, the role played by the alphabet size in network coding.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121390079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Barbier, C. Lucibello, Luca Saglietti, F. Krzakala, L. Zdeborová
{"title":"Compressed sensing with ℓ0-norm: statistical physics analysis & algorithms for signal recovery","authors":"D. Barbier, C. Lucibello, Luca Saglietti, F. Krzakala, L. Zdeborová","doi":"10.1109/ITW55543.2023.10161684","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161684","url":null,"abstract":"Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently, the algorithm offering the best tradeoff between compression rate, robustness, and speed for compressive sensing is the LASSO (ℓ1-norm bias) algorithm. However, many studies have pointed out the possibility that the implementation of ℓp-norms biases, with p smaller than one, could give better performance while sacrificing convexity. In this work, we focus specifically on the extreme case of the ℓ0-based reconstruction, a task that is complicated by the discontinuity of the loss. In the first part of the paper, we describe via statistical physics methods, and in particular the replica method, how the solutions to this optimization problem are arranged in a clustered structure. We observe two distinct regimes: one at low compression rate where the signal can be recovered exactly, and one at high compression rate where the signal cannot be recovered accurately. In the second part, we present two message-passing algorithms based on our first results for the ℓ0-norm optimization problem. The proposed algorithms are able to recover the signal at compression rates higher than the ones achieved by LASSO while being computationally efficient.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121558899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Deterministic K-Identification For Slow Fading Channels","authors":"Muris Spahovic, M. J. Salariseddigh, C. Deppe","doi":"10.1109/ITW55543.2023.10161643","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161643","url":null,"abstract":"Deterministic K-identification (DKI) is addressed for Gaussian channels with slow fading (GSF), where the transmitter is restricted to an average power constraint and channel side information is available at the decoder. We derive lower and upper bounds on the DKI capacity when the number of identifiable messages K may grow sub-linearly with the codeword length n. As a key finding, we establish that for deterministic encoding, assuming that the number of identifiable messages K = 2κ log n with κ ∈ [0, 1) being the identification target rate, the codebook size scales as 2(n log n)R, where R is the coding rate.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115508973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hyperbolic Sets in Incomplete Tables","authors":"J. J. Bernal, J. Simón","doi":"10.1109/ITW55543.2023.10161663","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161663","url":null,"abstract":"In this paper, we extend results about the implementation of the Berlekamp-Massey-Sakata algorithm on data tables having a number of unknown values.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"369 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122768429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the State Estimation Error of \"Beam-Pointing\" Channels: The Binary Case","authors":"Siyao Li, G. Caire","doi":"10.1109/ITW55543.2023.10161660","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161660","url":null,"abstract":"Sensing capabilities as an integral part of the network have been identified as a novel feature of sixth-generation (6G) wireless networks. As a key driver, millimeter-wave (mmWave) communication largely boosts speed, capacities, and connectivity. In order to maximize the potential of mmWave communication, precise and fast beam acquisition (BA) is crucial, since it compensates for a high pathloss and provides a large beamforming gain. Practically, the angle-of-departure (AoD) remains almost constant over numerous consecutive time slots, the backscatter signal experiences some delay, and the hardware is restricted under the peak power constraint. This work captures these main features by a simple binary beam-pointing (BBP) channel model with in-block memory (iBM) [1], peak cost constraint, and one unit-delayed feedback. In particular, we focus on the sensing capabilities of such a model and characterize the performance of the BA process in terms of the Hamming distortion of the estimated channel state. We encode the position of the AoD and derive the minimum distortion of the BBP channel under the peak cost constraint with no communication constraint. Our previous work [2] proposed a joint communication and sensing (JCAS) algorithm, which achieves the capacity of the same channel model. Herein, we show that by employing this JCAS transmission strategy, optimal data communication and channel estimation can be accomplished simultaneously. This yields the complete characterization of the capacity-distortion tradeoff for this model.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125257144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sebastian Bitzer, Julian Renner, A. Wachter-Zeh, Violetta Weger
{"title":"Generic Decoding in the Cover Metric","authors":"Sebastian Bitzer, Julian Renner, A. Wachter-Zeh, Violetta Weger","doi":"10.1109/ITW55543.2023.10160246","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10160246","url":null,"abstract":"Properties of random codes endowed with the cover metric are considered. We prove the NP-hardness of the decoding problem and then provide a generic decoder, following the information set decoding idea from Prange’s algorithm in the Hamming metric. Despite the cover metric lying between the Hamming and the rank metric, the complexity analysis of the algorithm reveals a significant difference between the metrics.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128027285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalization Properties of Adversarial Training for -ℓ0 Bounded Adversarial Attacks","authors":"Payam Delgosha, Hamed Hassani, Ramtin Pedarsani","doi":"10.1109/ITW55543.2023.10161648","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161648","url":null,"abstract":"We have widely observed that neural networks are vulnerable to small additive perturbations to the input causing misclassification. In this paper, we focus on the ℓ0-bounded adversarial attacks, and aim to theoretically characterize the performance of adversarial training for an important class of truncated classifiers. Such classifiers are shown to have strong performance empirically, as well as theoretically in the Gaussian mixture model, in the ℓ0-adversarial setting. The main contribution of this paper is to prove a novel generalization bound for the binary classification setting with ℓ0-bounded adversarial perturbation that is distribution-independent. Deriving a generalization bound in this setting has two main challenges: (i) the truncated inner product which is highly non-linear; and (ii) maximization over the ℓ0 ball due to adversarial training is non-convex and highly non-smooth. To tackle these challenges, we develop new coding techniques for bounding the combinatorial dimension of the truncated hypothesis class.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128488535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"State Estimation Entropy for Two-State Markov Sources in Slotted ALOHA Random Access Channels","authors":"G. Cocco, A. Munari, G. Liva","doi":"10.1109/ITW55543.2023.10161627","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161627","url":null,"abstract":"We study a system in which terminals monitoring two-state Markov sources communicate towards a common receiver over a slotted ALOHA random access channel. We analyze the system performance in terms of state estimation entropy (SEE), which measures the uncertainty at the receiver about the sources’ state. Two channel access strategies are studied, one that is influenced by the source behaviour and one that is independent of it. By means of density evolution analysis, we show that the former can yield a remarkable reduction of the SEE.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"29 Suppl 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131013066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Combinatorial Proof for the Dowry Problem","authors":"Xujun Liu, O. Milenkovic, G. Moustakides","doi":"10.1109/ITW55543.2023.10161638","DOIUrl":"https://doi.org/10.1109/ITW55543.2023.10161638","url":null,"abstract":"The Secretary problem is a classical sequential decision-making question that can be succinctly described as follows: a set of rank-ordered applicants are interviewed sequentially for a single position. Once an applicant is interviewed, an immediate and irrevocable decision is made if the person is to be offered the job or not and only applicants observed so far can be used in the decision process. The problem of interest is to identify the stopping rule that maximizes the probability of hiring the highest-ranked applicant. A multiple-choice version of the Secretary problem, known as the Dowry problem, assumes that one is given a fixed integer budget for the total number of selections allowed to choose the best applicant. It has been solved using tools from dynamic programming and optimal stopping theory. We provide the first combinatorial proof for a related new query-based model for which we are allowed to solicit the response of an expert to determine if an applicant is optimal. Since the selection criteria differ from those of the Dowry problem, we obtain nonidentical expected stopping times.","PeriodicalId":439800,"journal":{"name":"2023 IEEE Information Theory Workshop (ITW)","volume":"1040 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120876389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}